Complex networked systems are prevalent in biology, engineering, and the social sciences, yet their high-dimensional, nonlinear dynamics pose major challenges for analysis and prediction. A mathematically rigorous route to simplification is to represent system behavior on a low-dimensional, smooth invariant manifold known as a spectral submanifold (SSM). Here we present a comprehensive SSM reduction framework and its globalized extension (gSSM) for dimensionality reduction in large-scale nonlinear networks. Our approach yields accurate global and node-level predictions across synthetic and real networks, including highly heterogeneous topologies and systems with higher-order interactions. Crucially, SSM is a robust tipping-point predictor: even at low truncation order [e.g., $O\left(2\right)$] it reliably identifies the onset of sustained activity, while higher orders and gSSM capture postonset amplitudes and saturation. Consistently, the reduction collapses the full network dynamics to a one-dimensional system, offering clarity and efficiency. Across all the realizations, SSM and gSSM consistently outperform classical spectral and mean-field methods in modeling critical transitions at both microscopic and macroscopic scales, establishing SSM-based reduction as a robust, interpretable tool for nonlinear networked systems with broad applicability to epidemiology, ecology, and engineered networks.

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• Bifurcations
• Spreading
• Dynamical systems
• Scale free & inhomogeneous networks
• Small-world networks
• Social networks